an:03999488
Zbl 0616.76007
Johnson, R. E.; McMeeking, R. M.
Near-surface flow in glaciers obeying Glen's law
EN
Q. J. Mech. Appl. Math. 37, 273-291 (1984).
00149168
1984
j
76A05 86A60
gravity-driven flow; Glen's flow law; infinite longitudinal stress; glacier's surface; method of matched asymptotic expansions; near-surface region; a steady-state glacier; boundary-layer region
In determining the gravity-driven flow of a glacier or ice sheet which obeys Glen's flow law, previous methods have predicted infinite longitudinal stress at the glacier's surface. This physically unacceptable occurrence is due to a break-down in the mathematical methods used to obtain the solution. Using the method of matched asymptotic expansions, the solution valid in the near-surface region of a steady-state glacier is determined. The size of the near-surface or boundary-layer region is found to be of order delta 1n, where \(delta=h0/L\) is the assumed small ratio of the characteristic thickness and length of the ice sheet and n is the exponent in Glen's power law. The solution is obtained for ice sheets on both a steep and gentle base slope. The stress field in the near-surface region is obtained and we find that the boundary layer does not significantly affect the surface velocities or the glacier profile.